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Understand Unit Rate Concept - 6th Grade Math

  1. A recipe uses 3 cups of flour for every 4 cups of sugar. What is the unit rate of flour per 1 cup of sugar?
    Answer: 34\tfrac{3}{4} cup flour per cup sugar This question tests understanding of unit rate as the amount of flour per one cup of sugar, using rate language like 'per' in the context of recipes. The ratio of 3 cups flour to 4 cups sugar becomes a unit rate by dividing 3 by 4, resulting in 3/4 cup flour per cup sugar, meaning 3/4 cup flour for each one cup sugar. Rate language includes 'per' or 'for each,' such as '3/4 cup flour per cup sugar' or 'for each cup of sugar, use 3/4 cup flour.' Units are essential: 3/4 cups flour per cup sugar (cups/cup). Calculation: divide flour by sugar (3 ÷ 4 = 0.75 or 3/4). For example, 3 cups flour for 4 cups sugar calculates to 3÷4=3/4, so the unit rate is 3/4 cup flour per cup sugar (for each cup of sugar, use 3/4 cup flour). The correct unit rate is 3/4 cup flour per cup sugar with proper language and units. A common error is stating the ratio like 3:4 instead of the unit rate, or taking the reciprocal 4/3 cups sugar per cup flour, or using decimals incorrectly like 0.34. To find the unit rate: (1) identify the ratio (3:4 flour to sugar), (2) divide first by second (3÷4=3/4), (3) express with units (3/4 cup flour per cup sugar), (4) use rate language ('3/4 cup flour per cup sugar'). Interpretation: this unit rate tells that for each cup of sugar, you need 3/4 cup of flour. Ratio vs unit rate: ratio compares (3:4), unit rate simplifies to per-unit (3/4 per).
  2. There are 24 students in a club with 3 adult volunteers. What is the unit rate in students per volunteer?
    Answer: 8 students per volunteer This question tests understanding of unit rate as the amount of students per one volunteer, using rate language like 'per' in the context of group ratios. The ratio of 24 students to 3 volunteers becomes a unit rate by dividing 24 by 3, resulting in 8 students per volunteer, meaning 8 students for each one volunteer. Rate language includes 'per' or 'for each,' such as '8 students per volunteer' or 'for each volunteer, there are 8 students.' Units are essential: 8 students per volunteer. Calculation: divide students by volunteers (24 ÷ 3 = 8). For example, 24 students with 3 volunteers calculates to 24÷3=8, so the unit rate is 8 students per volunteer (each volunteer handles 8 students). The correct unit rate is 8 students per volunteer with proper language and units. A common error is reversing to 3/24=0.125 volunteers per student, or stating the ratio 24:3, or subtracting like 24-3=21. To find the unit rate: (1) identify the ratio (24:3 students to volunteers), (2) divide first by second (24÷3=8), (3) express with units (8 students per volunteer), (4) use rate language ('8 students per volunteer'). Interpretation: this unit rate tells that each volunteer is responsible for 8 students. Ratio vs unit rate: ratio compares (24:3), unit rate simplifies to per-unit (8 per).
  3. The graph shows the relationship between time and distance for a jogger running at a constant speed. What is the jogger's unit rate, and what does it represent?
    Answer: 6 miles per hour, representing the distance traveled in one hour of jogging From the graph, the jogger travels 3 miles in 30 minutes (0.5 hours). The unit rate for speed is 3 miles ÷ 0.5 hours = 6 miles per hour, which represents distance per unit time. Choice B gives time per distance (the reciprocal) rather than the standard speed unit rate. Choice C also gives time per distance, just in decimal form. Choice D gives a rate but not a unit rate since it uses 30 minutes rather than 1 hour as the time unit.
  4. A video game download takes 30 minutes for 6 gigabytes. What is the unit rate in gigabytes per minute?
    Answer: 0.2 gigabytes per minute This question tests understanding of unit rate as the amount of gigabytes per one minute, using rate language like 'per' in the context of download speed. The ratio of 6 gigabytes to 30 minutes becomes a unit rate by dividing 6 by 30, resulting in 0.2, which means 0.2 gigabytes per minute or 0.2 gigabytes for each one minute; rate language includes 'per' or 'for each,' and units are essential, such as gigabytes per minute. For example, with 6 gigabytes in 30 minutes, calculate 6 ÷ 30 = 0.2, so the unit rate is 0.2 gigabytes per minute (downloads 0.2 gigabytes in each minute). The correct unit rate is 0.2 gigabytes per minute. A common error is subtracting like 30 - 6 = 24, or inverting to minutes per gigabyte, or omitting units and 'per' language. To find the unit rate: (1) identify the ratio (6:30 gigabytes to minutes), (2) divide gigabytes by minutes (6 ÷ 30 = 0.2), (3) express with units (0.2 gigabytes per minute), (4) use rate language ('0.2 gigabytes per minute'). This unit rate tells the download amount per one minute, simplifying the total into a per-unit rate for comparison.
  5. Maya mixed paint using 4 parts blue paint to 6 parts white paint. She used 20 ounces of blue paint total. Which statement correctly describes a unit rate for this mixture and its application?
    Answer: The ratio gives 1.5 ounces of white paint per ounce of blue paint, so she used 30 ounces of white paint When you see a ratio problem like this, you need to find the unit rate (how much of one thing per one unit of another) and then scale it up to the actual amounts used. Maya's paint mixture has a ratio of 4 parts blue to 6 parts white. To find the unit rate of white paint per blue paint, you divide: 6 parts white4 parts blue=1.5\frac{6 \text{ parts white}}{4 \text{ parts blue}} = 1.5 ounces of white paint per ounce of blue paint. Since Maya used 20 ounces of blue paint, you multiply: 20×1.5=3020 \times 1.5 = 30 ounces of white paint. Answer A incorrectly calculates the unit rate as 64=1.5\frac{6}{4} = 1.5, but then somehow gets 2.5. This leads to the wrong final amount of 50 ounces. Answer B flips the ratio backwards, calculating 46=0.67\frac{4}{6} = 0.67 ounces of blue per ounce of white instead of white per blue. This fundamental error makes the entire calculation meaningless for this problem. Answer D completely misunderstands ratios by claiming 4 ounces of blue per ounce of white, which would mean blue paint is more concentrated than the original 4:6 ratio suggests. The resulting 5 ounces of white paint is far too small. Answer C correctly identifies the unit rate as 1.5 ounces of white per ounce of blue and properly applies it to get 30 ounces of white paint. Strategy tip: Always write out your unit rate as a fraction first, then convert to decimal. Double-check that your final amounts make sense compared to the original ratio.
  6. A recipe uses 3 cups of flour for every 4 cups of sugar. What is the unit rate of flour per 1 cup of sugar?
    Answer: 34\frac{3}{4} cup flour per cup sugar This question tests understanding of unit rate as the amount of flour per one cup of sugar, using rate language like 'per' in the context of recipes. The ratio of 3 cups flour to 4 cups sugar becomes a unit rate by dividing 3 by 4, resulting in 3/4, which means 3/4 cup flour per cup sugar or 3/4 cup flour for each one cup sugar; rate language includes 'per' or 'for each,' and units are essential, such as cups flour per cup sugar. For example, with 3 cups flour for 4 cups sugar, calculate 3 ÷ 4 = 3/4, so the unit rate is 3/4 cup flour per cup sugar (for each cup of sugar, use 3/4 cup flour). The correct unit rate is 3/4 cup flour per cup sugar. A common error is stating the reciprocal as 4/3 instead of 3/4, or leaving it as the ratio 3:4 without dividing, or reversing the direction to sugar per flour. To find the unit rate: (1) identify the ratio (3:4 flour to sugar), (2) divide flour by sugar (3 ÷ 4 = 3/4), (3) express with units (3/4 cup flour per cup sugar), (4) use rate language ('3/4 cup flour per cup sugar'). This unit rate tells the amount of flour needed per one cup of sugar, distinguishing it from the overall ratio.
  7. A cyclist rides 180 miles in 3 hours. What is the unit rate, in miles per hour?
    Answer: 60 miles per hour This question tests understanding of unit rate as the amount of miles per one hour, using rate language like 'per' in the context of cycling speed. The ratio of 180 miles to 3 hours becomes a unit rate by dividing 180 by 3, resulting in 60, which means 60 miles per hour or 60 miles for each one hour; rate language includes 'per' or 'for each,' and units are essential, such as miles per hour (mph). For example, with 180 miles in 3 hours, calculate 180 ÷ 3 = 60, so the unit rate is 60 miles per hour (travel 60 miles in each hour). The correct unit rate is 60 miles per hour. A common error is stating the ratio as 180:3 without dividing, or adding like 180 + 3 = 183, or inverting to hours per mile. To find the unit rate: (1) identify the ratio (180:3 miles to hours), (2) divide miles by hours (180 ÷ 3 = 60), (3) express with units (60 miles per hour), (4) use rate language ('60 miles per hour'). This unit rate tells the speed per one hour, simplifying the total journey into a per-unit measure.
  8. A painter uses 22 gallons of paint to cover 55 walls. How many gallons of paint is that per 1 wall?
    Answer: 25\frac{2}{5} gallon per wall This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in usage contexts. A ratio like 2:5 gallons to walls becomes a unit rate by dividing 2 by 5, giving 2/5 gallon per wall or 0.4 gallons for each wall. Rate language should include 'per' or 'for each,' such as '2/5 gallon per wall,' and units are essential, like gallons per wall. The calculation involves dividing the first quantity by the second: 2 ÷ 5 = 2/5. For example, with 2 gallons for 5 walls, calculate 2 ÷ 5 = 2/5, so the unit rate is 2/5 gallon per wall, meaning each wall requires 2/5 gallon. The correct unit rate is 2/5 gallon per wall. A common error is taking the reciprocal like 5/2 gallons per wall, reversing to walls per gallon like 5/2, omitting units like just '2/5,' or wrong like 2+1=3. To find the unit rate: (1) identify the ratio (2:5 gallons to walls), (2) divide first by second (2 ÷ 5 = 2/5), (3) express with units (2/5 gallon per wall), (4) use rate language ('2/5 gallon per wall'). Interpretation: the unit rate tells that for each 1 wall, 2/5 gallon is used. Ratio compares totals (2:5), while unit rate simplifies to per unit (2/5 per). Common contexts include usage rates, like paint per surface.
  9. A movie theater sells 15 tickets for $120. Which statement correctly gives the unit rate using rate language?
    Answer: $8 per ticket This question tests understanding of unit rate as the amount of dollars per one ticket, using rate language like 'per' in the context of ticket pricing. The ratio of $120 to 15 tickets becomes a unit rate by dividing 120 by 15, resulting in 8, which means $8 per ticket or 8foreachoneticket;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarsperticket(8 for each one ticket; rate language includes 'per' or 'for each,' and units are essential, such as dollars per ticket (/ticket). For example, with $120 for 15 tickets, calculate 120 ÷ 15 = 8, so the unit rate is $8 per ticket (each ticket costs $8). The correct statement is $8 per ticket, which properly uses rate language and units. A common error is leaving it as the ratio $120 per 15 tickets without dividing, or miscalculating like 120 ÷ 15 = 60, or omitting 'per' making it unclear. To find the unit rate: (1) identify the ratio (120:15 dollars to tickets), (2) divide dollars by tickets (120 ÷ 15 = 8), (3) express with units ($8 per ticket), (4) use rate language ('$8 per ticket'). This unit rate tells the cost per one ticket, distinguishing it from the bulk price ratio.
  10. A bottle holds 1212 ounces of juice and costs $3. What is the unit rate in dollars per ounce?
    Answer: $0.25 per ounce This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in pricing contexts. A ratio like 3:12 dollars to ounces becomes a unit rate by dividing 3 by 12, giving 0.25 dollars per ounce or $0.25 for each ounce. Rate language should include 'per' or 'for each,' such as '0.25perounce,′andunitsareessential,likedollarsperounce(0.25 per ounce,' and units are essential, like dollars per ounce (/oz). The calculation involves dividing the first quantity by the second: 3 ÷ 12 = 0.25. For example, with $3 for 12 ounces, calculate 3 ÷ 12 = 0.25, so the unit rate is $0.25 per ounce, meaning each ounce costs $0.25. The correct unit rate is $0.25 per ounce. A common error is reversing to ounces per dollar like 12/3=4, stating the ratio 3:12, omitting units like just '0.25,' or wrong math like 3/8.333≈0.36. To find the unit rate: (1) identify the ratio (3:12 dollars to ounces), (2) divide first by second (3 ÷ 12 = 0.25), (3) express with units ($0.25 per ounce), (4) use rate language ('$0.25 per ounce'). Interpretation: the unit rate tells that for each 1 ounce, the cost is $0.25. Ratio compares totals (3:12), while unit rate simplifies to per unit (0.25 per). Common contexts include cost per unit, like dollars per ounce in products.
  11. A coach buys 14 water bottles for $49. What is the unit rate in dollars per bottle?
    Answer: $3.50 per bottle This question tests understanding of unit rate as the amount of dollars per one bottle, using rate language like 'per' in the context of bulk purchases. The ratio of $49 to 14 bottles becomes a unit rate by dividing 49 by 14, resulting in $3.50 per bottle, meaning $3.50 for each one bottle. Rate language includes 'per' or 'for each,' such as '$3.50 per bottle' or 'for each bottle, it costs $3.50.' Units are essential: 3.50perbottle(3.50 per bottle (/bottle). Calculation: divide dollars by bottles (49 ÷ 14 = 3.5). For example, $49 for 14 bottles calculates to 49÷14=3.5, so the unit rate is $3.50 per bottle (each bottle costs $3.50). The correct unit rate is $3.50 per bottle with proper language and units. A common error is dividing incorrectly like 14/49≈0.286 bottles per dollar, or rounding wrong like $3, or stating the ratio $49:14. To find the unit rate: (1) identify the ratio (49:14 dollars to bottles), (2) divide first by second (49÷14=3.5), (3) express with units (3.50 dollars per bottle), (4) use rate language ('costs $3.50 per bottle'). Interpretation: this unit rate tells that each bottle costs $3.50. Ratio vs unit rate: ratio compares (49:14), unit rate simplifies to per-unit (3.5 per).
  12. A runner travels 180180 miles in 33 hours. What is the unit rate in miles per hour?
    Answer: 6060 miles per hour This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in speed contexts. A ratio like 180:3 miles to hours becomes a unit rate by dividing 180 by 3, giving 60 miles per hour or 60 mph for each hour. Rate language should include 'per' or 'for each,' such as '60 miles per hour,' and units are essential, like miles per hour (mph). The calculation involves dividing the first quantity by the second: 180 ÷ 3 = 60. For example, with 180 miles in 3 hours, calculate 180 ÷ 3 = 60, so the unit rate is 60 miles per hour, meaning 60 miles traveled for each hour. The correct unit rate is 60 miles per hour. A common error is adding like 180+3=183, dividing wrong like 3/180=1/60 or 180/2=90, omitting units like just '60,' or reversing to hours per mile. To find the unit rate: (1) identify the ratio (180:3 miles to hours), (2) divide first by second (180 ÷ 3 = 60), (3) express with units (60 miles per hour), (4) use rate language ('60 miles per hour'). Interpretation: the unit rate tells that in each 1 hour, 60 miles are traveled. Ratio compares totals (180:3), while unit rate simplifies to per unit (60 per). Common contexts include speed, like distance per time.
  13. A video game downloads 600 megabytes in 5 minutes. What is the unit rate in megabytes per minute?
    Answer: 120 megabytes per minute This question tests understanding of unit rate as the amount of megabytes per one minute, using rate language like 'per' in the context of download speeds. The ratio of 600 megabytes to 5 minutes becomes a unit rate by dividing 600 by 5, resulting in 120 megabytes per minute, meaning 120 megabytes for each one minute. Rate language includes 'per' or 'for each,' such as '120 megabytes per minute' or 'for each minute, downloads 120 megabytes.' Units are essential: 120 megabytes per minute (MB/min). Calculation: divide megabytes by minutes (600 ÷ 5 = 120). For example, 600 megabytes in 5 minutes calculates to 600÷5=120, so the unit rate is 120 megabytes per minute (downloads 120 MB each minute). The correct unit rate is 120 megabytes per minute with proper language and units. A common error is stating the ratio like 600:5, or reversing to 5/600 minutes per megabyte, or miscalculating as 600×5=3000. To find the unit rate: (1) identify the ratio (600:5 megabytes to minutes), (2) divide first by second (600÷5=120), (3) express with units (120 megabytes per minute), (4) use rate language ('120 megabytes per minute'). Interpretation: this unit rate tells that in each minute, 120 megabytes are downloaded. Ratio vs unit rate: ratio compares (600:5), unit rate simplifies to per-unit (120 per).
  14. A paint mixture uses 5 cups of blue paint for every 2 cups of white paint. What does the unit rate 52\frac{5}{2} mean in this situation?
    Answer: There are 52\frac{5}{2} cups of blue paint per 1 cup of white paint. This question tests understanding of unit rate as the amount of blue paint per one cup of white paint, using rate language like 'per' or 'for each' in the context of mixtures. The ratio of 5 cups blue to 2 cups white becomes a unit rate by dividing 5 by 2, resulting in 5/2, which means 5/2 cups blue per cup white or 5/2 cups blue for each one cup white; rate language includes 'per' or 'for each,' and units are essential, such as cups blue per cup white. For example, with 5 cups blue for 2 cups white, calculate 5 ÷ 2 = 5/2, so the unit rate is 5/2 cups blue paint per cup white (for each cup of white, use 5/2 cups blue). The correct interpretation is there are 5/2 cups of blue paint per 1 cup of white paint. A common error is subtracting like 5 - 2 = 3, or stating the ratio without dividing, or reversing to white per blue. To find the unit rate: (1) identify the ratio (5:2 blue to white), (2) divide blue by white (5 ÷ 2 = 5/2), (3) express with units (5/2 cups blue per cup white), (4) use rate language ('5/2 cups of blue paint per 1 cup of white paint'). This unit rate explains the mixture per one unit of white paint, clarifying the proportion in words.
  15. A school store sells 12 notebooks for $18. What is the unit rate, in dollars per notebook?
    Answer: $1.50 per notebook This question tests understanding of unit rate as the amount of dollars per one notebook, using rate language like 'per' in the context of pricing. The ratio of $18 to 12 notebooks becomes a unit rate by dividing 18 by 12, resulting in 1.5, which means $1.50 per notebook or 1.50foreachonenotebook;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarspernotebook(1.50 for each one notebook; rate language includes 'per' or 'for each,' and units are essential, such as dollars per notebook (/notebook). For example, with $18 for 12 notebooks, calculate 18 ÷ 12 = 1.5, so the unit rate is $1.50 per notebook (each notebook costs $1.50). The correct unit rate is $1.50 per notebook. A common error is stating the ratio as 12:18 instead of the unit rate, or reversing to find notebooks per dollar, or omitting units like just saying '1.50' without specifying dollars per notebook. To find the unit rate: (1) identify the ratio (18:12 dollars to notebooks), (2) divide dollars by notebooks (18 ÷ 12 = 1.5), (3) express with units ($1.50 per notebook), (4) use rate language ('costs $1.50 per notebook'). This unit rate tells the cost per one notebook, simplifying the comparison from the total ratio.
  16. A class has 24 students and 3 teachers. What is the unit rate of students per teacher?
    Answer: 8 students per teacher This question tests understanding of unit rate as the amount of students per one teacher, using rate language like 'per' in the context of class ratios. The ratio of 24 students to 3 teachers becomes a unit rate by dividing 24 by 3, resulting in 8, which means 8 students per teacher or 8 students for each one teacher; rate language includes 'per' or 'for each,' and units are essential, such as students per teacher. For example, with 24 students and 3 teachers, calculate 24 ÷ 3 = 8, so the unit rate is 8 students per teacher (each teacher has 8 students). The correct unit rate is 8 students per teacher. A common error is reversing to teachers per student like 3/24, or stating the ratio as 24:3 without dividing, or subtracting like 24 - 3 = 21. To find the unit rate: (1) identify the ratio (24:3 students to teachers), (2) divide students by teachers (24 ÷ 3 = 8), (3) express with units (8 students per teacher), (4) use rate language ('8 students per teacher'). This unit rate tells the number of students per one teacher, making it easier to compare class sizes than the total ratio.
  17. A bus travels 9696 miles in 22 hours. What is the unit rate in miles per hour?
    Answer: 4848 miles per hour This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in speed contexts. A ratio like 96:2 miles to hours becomes a unit rate by dividing 96 by 2, giving 48 miles per hour or 48 mph for each hour. Rate language should include 'per' or 'for each,' such as '48 miles per hour,' and units are essential, like miles per hour (mph). The calculation involves dividing the first quantity by the second: 96 ÷ 2 = 48. For example, with 96 miles in 2 hours, calculate 96 ÷ 2 = 48, so the unit rate is 48 miles per hour, meaning 48 miles traveled each hour. The correct unit rate is 48 miles per hour. A common error is adding like 96-2=94 or 96*2=192, reducing wrong like 2/96, omitting units like just '48,' or reversing direction. To find the unit rate: (1) identify the ratio (96:2 miles to hours), (2) divide first by second (96 ÷ 2 = 48), (3) express with units (48 miles per hour), (4) use rate language ('48 miles per hour'). Interpretation: the unit rate tells that in each 1 hour, 48 miles are traveled. Ratio compares totals (96:2), while unit rate simplifies to per unit (48 per). Common contexts include transportation speed, like miles per hour.
  18. At a fruit stand, apples cost $4.50 for 3 pounds and oranges cost $6.40 for 4 pounds. Sarah wants to buy 5 pounds of the cheaper fruit. How much will she spend?
    Answer: $7.50 because apples cost $1.50 per pound and 5 × $1.50 = $7.50 When you encounter word problems involving rates and unit prices, you need to find the cost per unit first, then compare to determine which option is cheaper. Let's calculate the cost per pound for each fruit. For apples: $4.503 pounds=$1.50 per pound\frac{\$4.50}{3 \text{ pounds}} = \$1.50 \text{ per pound}. For oranges: $6.404 pounds=$1.60 per pound\frac{\$6.40}{4 \text{ pounds}} = \$1.60 \text{ per pound}. Since apples cost $1.50 per pound and oranges cost $1.60 per pound, apples are the cheaper fruit. Sarah wants 5 pounds of the cheaper fruit (apples), so her total cost is: 5×$1.50=$7.505 \times \$1.50 = \$7.50 Now let's examine why the other answers are wrong. Choice A incorrectly states that oranges cost $1.50 per pound—this is actually the price of apples. The calculation is right, but it's applied to the wrong fruit. Choice B correctly calculates that oranges cost $1.60 per pound, but oranges aren't the cheaper option, so Sarah wouldn't buy them. Choice C makes a calculation error by claiming apples cost $1.60 per pound, which is actually the price of oranges. Choice D correctly identifies that apples cost $1.50 per pound, recognizes that apples are cheaper than oranges, and properly calculates the total cost as $7.50. Study tip: In multi-step word problems, work systematically: calculate all unit rates first, compare them to find what you're looking for, then do your final calculation. Double-check that you're using the right numbers for the right items—mixing up which price belongs to which option is a common mistake.
  19. A pack of markers costs $14 for 7 markers. What is the unit rate in dollars per marker?
    Answer: $2 per marker This question tests understanding of unit rate as the amount of dollars per one marker, using rate language like 'per' in the context of unit pricing. The ratio of $14 to 7 markers becomes a unit rate by dividing 14 by 7, resulting in 2, which means $2 per marker or 2foreachonemarker;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarspermarker(2 for each one marker; rate language includes 'per' or 'for each,' and units are essential, such as dollars per marker (/marker). For example, with $14 for 7 markers, calculate 14 ÷ 7 = 2, so the unit rate is $2 per marker (each marker costs $2). The correct unit rate is $2 per marker. A common error is stating the ratio as 14:7 without dividing, or reversing to markers per dollar like 7/14 = 0.50, or adding instead of dividing. To find the unit rate: (1) identify the ratio (14:7 dollars to markers), (2) divide dollars by markers (14 ÷ 7 = 2), (3) express with units ($2 per marker), (4) use rate language ('$2 per marker'). This unit rate tells the cost per one marker, making it distinct from the pack ratio for individual pricing.
  20. A school store sells 99 notebooks for $27. What is the unit rate in dollars per notebook?
    Answer: $3 per notebook This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in pricing contexts. A ratio like 27:927:9 dollars to notebooks becomes a unit rate by dividing 2727 by 99, giving 33 dollars per notebook or 33 for each notebook. Rate language should include 'per' or 'for each,' such as '33 per notebook,' and units are essential, like dollars per notebook ($/notebook). The calculation involves dividing the first quantity by the second: 27÷9=327 ÷ 9 = 3. For example, with 2727 for 99 notebooks, calculate 27÷9=327 ÷ 9 = 3, so the unit rate is 33 per notebook, meaning each notebook costs 33. The correct unit rate is 33 per notebook. A common error is reversing to notebooks per dollar like 9/27=1/39/27=1/3, stating the ratio 27:927:9, omitting units like just '3,' or multiplying 27/1.5=1827/1.5=18 or adding to 27+9/27+9/ something$= something. To find the unit rate: (1) identify the ratio (27:927:9 dollars to notebooks), (2) divide first by second (27÷9=327 ÷ 9 = 3), (3) express with units (33 per notebook), (4) use rate language ('33 per notebook'). Interpretation: the unit rate tells that for each 1 notebook, the cost is 33. Ratio compares totals (27:927:9), while unit rate simplifies to per unit (33 per). Common contexts include school supplies pricing, like cost per item.

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